In this section, we use the Hubble radius (\(L=H^{-1}\) ) as IR
cutoff to study the effects of a sign-changeable interaction in
the HDE model. In this case we have \(\rho _D=3c^2M_p^2H^2\) , where
\(c\)  is a constant. Finally, bearing the
\(\Omega _D={\rho _D}/{(3M_p^2H^2)}\)  relation in mind, we find out
\(\Omega _D=c^2\)  meaning that \(c^2\)  should meet the \(0\le c^2\le 1\) 
condition [1]}. It is worth mentioning that, in the
non-interacting model we arrive at \(\omega _D=0\)  for the HDE with
Hubble radius as the IR cutoff [2]}. This implies that in
this case the accelerated expansion of the universe cannot be
achieved [2]}. It is also a matter of calculation to
combine the \(\rho _D=3c^2M_p^2H^2\)  expression with
Eqs. () and (REF ), and using the \(Q = 3 b^2Hq\rho =3 b^2 Hq(\rho _D+\rho _m)\)  relation for the mutual
interaction to get
\(\omega _D=-\frac{ b^2 q}{c^2(1-c^2)},\) 
